A reduced variable neighborhood search algorithm for uncapacitated multilevel lot-sizing problems

Multilevel lot-sizing (MLLS) problems, which involve complicated product structures with interdependence among the items, play an important role in the material requirement planning (MRP) system of modern manufacturing/assembling lines. In this paper, we present a reduced variable neighborhood search (RVNS) algorithm and several implemental techniques for solving uncapacitated MLLS problems. Computational experiments are carried out on three classes of benchmark instances under different scales (small, medium, and large). Compared with the existing literature, RVNS shows good performance and robustness on a total of 176 tested instances. For the 96 small-sized instances, the RVNS algorithm can find 100% of the optimal solutions in less computational time; for the 40 medium-sized and the 40 large-sized instances, the RVNS algorithm is competitive against other methods, enjoying good effectiveness as well as high computational efficiency. In the calculations, RVNS updated 7 (17.5%) best known solutions for the medium-sized instances and 16 (40%) best known solutions for the large-sized instances.